For weak gravitational field the frequency ratio between top and bottom is ft/fb = (1 + Rs/2rt - Rs/2rb) where Rs is Schwarzschild radius, rt and rb distance from centre of body (earth centre). From there, sorry this is French wikipedia, I don't find a convenient English resource for the same formula.

For Earth Rs is about 9mm, so lets say we have 0.3m altitude difference at earth surface (6.371e6m) => ft/fb = 1 - 3.3e-17This is one part in 3e16 redshift in frequency.

Likewise any Doppler effect affecting the relative wavelengths (momentums) of photons between forward and backward plates of an accelerating frustum would indeed induce a non 0 net force : this force would always be opposite to the acceleration (ie. never a thrust) and in fact could be interpreted as the inertia of the mass equivalent of energy bouncing back and forth in the cavity (whatever its shape). The time constant of a photon in a Q=10000 about 0.3m across frustum would be like 10µs, at 100W pumped into the frustum there is then on the order of 1e-3 J EM energy content at any given time, that is equivalent to 1.1e-20 kg of mass, or an apparent added "force of inertia" of 1.1e-19N for a spacecraft accelerating at 1g, or equivalently an added weight of 1.1e-19N vertically for a resting frustum on earth.

In summary, within classical frameworks, yes there can be non 0 net force of EM radiation in an accelerating cavity, but this will be vanishingly small forces, and always opposite to acceleration (aka "inertia").Is it correct ?

Close, those forces are similar to the observed forces. Perhaps @Rodal has the page reference back to my calculation which is what I beleive you are stating.

What do you mean by "similar to the observed forces" ? Quantitatively what my very crude estimations of effect of acceleration on EM net force imbalance are 14 orders of magnitude below observed forces at EW, and that is for 1g acceleration, which is far from acceleration of the frustum (horizontal wise), even taking into account recorded noise.

I should really not put my feet in that but : if Doppler effects are to be given importance ( to the point of wanting to compensate for them ) and related influence of acceleration of device on resonance, then this should be quantitatively assessed. A 30cm journey from one end to the other takes a photon 1ns. In such a short time a 1g accelerating frustum would have added or subtracted only v=1e-8 m/s to the velocity seen by the photon on the "last bounce" (this is very crude !). What is the Doppler effect of such a tiny velocity difference ? f1/f0 = 1 +or- v/c that would amount to a ratio of 1 +or- 3.3e-17, in agreement with above value for gravitational redshift (equivalently, for the same 1g and 30cm distance). I fail to understand how even a superconducting cavity with a Q of a billion and a super narrow bandwidth would care about such a tiny Doppler shift...

And the net force imbalance induced by this Doppler shift, for 100W pumped into frustum at Q=10000 would be 1.1e-19N, at Q=1e9 would be 1.1e-14N ... (and opposite to acceleration). Basically this is just the "inertial force" of the equivalent EM mass multiplied by acceleration...

Beyond this crude photon model I must admit I don't get the more sophisticated equations, I know this was explained quite a bit. Notsosureofit would you care plugging the same parameters in your formulas and derive values, what a ~30cm frustum would experience as net EM force imbalance due to acceleration at 1g, given a feed of 100W at Q=10000 ? What is wrong with a crude photon model that don't show dependency on frequency that would be correct with your model where I see some f^3 but no acceleration ?

I have : F = - acc * P*Q*L/c^3 F net EM radiation imbalance due to acceleration of frustumacc acceleration in m/s²P input power in WL length of cavity in mc speed of light

This is not the levels of "thrust" (well, this is not a thrust at all !) experimentally recorded, but is it physically sound ?

Quote

Edit: I think this was it (have to check)

"The proposition that dispersion caused by an accelerating frame of reference implied an accelerating frame of reference caused by a dispersive cavity resonator. (to 1st order using massless, perfectly conducting cavity)

Rotate the dispersion relation of the cavity into doppler frame to get the Doppler shifts, that is to say, look at the dispersion curve intersections of constant wave number instead of constant frequency.

Zellerium, I am uncertain about if your University allows for this sort of thing or not, but for the purposes of the nascent Wiki under development, would you be willing to provide (later once you have them) some Bills of Materials as well as instructions documenting how you assembled and set up your rig?

...Dr. Rodal:Do you think the thrust signiture observed from the null Cannae drive could be due to air currents? I assume the frustum yielded similar thrusts while in a vacuum and in air, which shows how much the air is effecting thrust. Unless the shape of the Cannae drive led to a significant air current, it seems a symmetric cavity should produce thrust.

Although we may be able to find the resonant frequencies for the frustum using software, changing parameters like the dielectric thickness will change the frequency required. And if we have to use a microwave magnetron then we have to change the frustum's size which is more challenging, but still possible.However, if we recieve enough money for the variable frequency test a tapered cavity would be a much better option.

I just downloaded EM Pro recently, but I only have experience with 3-D design software (Creo) and Matlab. We may have licenses available for Multiphysics, I'll look into it.

...

Thermal convection forces have plagued radiation pressure measurements since the time of Maxwell, for about 139 years and counting. There is a rich history showing this.

The shape of the Cannae device maximizes the effect of thermal convection effects.

Please notice that the thrust/PowerInput obtained by NASA Eagleworks in a vacuum is only a fraction of the one that they measured in air, which shows quantitatively the huge problem with conducting tests under ambient conditions like Shawyer in the UK and Yang in China have done. But, again, if you don't have a vacuum chamber, there are proven ways to minimize this effect that neither Shawyer nor Yang appear to have utilized.

I advise against performing any Finite Element Analysis calculations unless you have an analyst available that has taken a University course in Finite Element Analysis and has practical experience with such Finite Element packages. If you need to perform FEA you must add to your team such an analyst.

EDIT: If you use the same geometrical dimensions and materials used by NASA, couldn't you use NASA's COMSOL calculations (available in this thread) to assess the frequencies and mode shapes ? (and thus avoid the need to perform any numerical calculations on your own)

Shawyers 1st EM Drive and test rig looks like something fairly simple to duplicate:http://emdrive.com/feasibilitystudy.htmlWhile sophistication is nice, to start off maybe better to go for KISS? Build what has been shown to work in both the drive and the measurement system. Is what my replication efforts will be following, with no new wheels invested until I have a few that work as Shawyer predicts.

One thing to note, the EM Drive was tested in a vertical orientation, pointed up, then down and the 2 thrust values averaged.

I've set up a MediaWiki server before and it wasn't too bad. That is a good platform. I'm simply stretched too thin right now to try it again.

I've lurked for the whole thread, but actually did create a media wiki server for this! Its located at http://tracket.co.

I've always wanted to create a distributed, public project management platform to help organize and promote collaboration in global academic and research efforts. Given the acceleration in knowledge generation, I felt that we could increase efficiency through more productive collaboration.

Edit: now that I've finished catching up with the last few pages, I see that a community member has already taken care of this. This wiki will remain online (as it has unused for a couple months) but feel free to ignore as you see fit.

For weak gravitational field the frequency ratio between top and bottom is ft/fb = (1 + Rs/2rt - Rs/2rb) where Rs is Schwarzschild radius, rt and rb distance from centre of body (earth centre). From there, sorry this is French wikipedia, I don't find a convenient English resource for the same formula.

For Earth Rs is about 9mm, so lets say we have 0.3m altitude difference at earth surface (6.371e6m) => ft/fb = 1 - 3.3e-17This is one part in 3e16 redshift in frequency.

Likewise any Doppler effect affecting the relative wavelengths (momentums) of photons between forward and backward plates of an accelerating frustum would indeed induce a non 0 net force : this force would always be opposite to the acceleration (ie. never a thrust) and in fact could be interpreted as the inertia of the mass equivalent of energy bouncing back and forth in the cavity (whatever its shape). The time constant of a photon in a Q=10000 about 0.3m across frustum would be like 10µs, at 100W pumped into the frustum there is then on the order of 1e-3 J EM energy content at any given time, that is equivalent to 1.1e-20 kg of mass, or an apparent added "force of inertia" of 1.1e-19N for a spacecraft accelerating at 1g, or equivalently an added weight of 1.1e-19N vertically for a resting frustum on earth.

In summary, within classical frameworks, yes there can be non 0 net force of EM radiation in an accelerating cavity, but this will be vanishingly small forces, and always opposite to acceleration (aka "inertia").Is it correct ?

Close, those forces are similar to the observed forces. Perhaps @Rodal has the page reference back to my calculation which is what I beleive you are stating.

What do you mean by "similar to the observed forces" ? Quantitatively what my very crude estimations of effect of acceleration on EM net force imbalance are 14 orders of magnitude below observed forces at EW, and that is for 1g acceleration, which is far from acceleration of the frustum (horizontal wise), even taking into account recorded noise.

I should really not put my feet in that but : if Doppler effects are to be given importance ( to the point of wanting to compensate for them ) and related influence of acceleration of device on resonance, then this should be quantitatively assessed. A 30cm journey from one end to the other takes a photon 1ns. In such a short time a 1g accelerating frustum would have added or subtracted only v=1e-8 m/s to the velocity seen by the photon on the "last bounce" (this is very crude !). What is the Doppler effect of such a tiny velocity difference ? f1/f0 = 1 +or- v/c that would amount to a ratio of 1 +or- 3.3e-17, in agreement with above value for gravitational redshift (equivalently, for the same 1g and 30cm distance). I fail to understand how even a superconducting cavity with a Q of a billion and a super narrow bandwidth would care about such a tiny Doppler shift...

And the net force imbalance induced by this Doppler shift, for 100W pumped into frustum at Q=10000 would be 1.1e-19N, at Q=1e9 would be 1.1e-14N ... (and opposite to acceleration). Basically this is just the "inertial force" of the equivalent EM mass multiplied by acceleration...

Beyond this crude photon model I must admit I don't get the more sophisticated equations, I know this was explained quite a bit. Notsosureofit would you care plugging the same parameters in your formulas and derive values, what a ~30cm frustum would experience as net EM force imbalance due to acceleration at 1g, given a feed of 100W at Q=10000 ? What is wrong with a crude photon model that don't show dependency on frequency that would be correct with your model where I see some f^3 but no acceleration ?

I have : F = - acc * P*Q*L/c^3 F net EM radiation imbalance due to acceleration of frustumacc acceleration in m/s²P input power in WL length of cavity in mc speed of light

This is not the levels of "thrust" (well, this is not a thrust at all !) experimentally recorded, but is it physically sound ?

Quote

Edit: I think this was it (have to check)

"The proposition that dispersion caused by an accelerating frame of reference implied an accelerating frame of reference caused by a dispersive cavity resonator. (to 1st order using massless, perfectly conducting cavity)

Rotate the dispersion relation of the cavity into doppler frame to get the Doppler shifts, that is to say, look at the dispersion curve intersections of constant wave number instead of constant frequency.

df = (1/(2*f))*(c/(2*Pi))^2*X^2*((1/Rs^2)-(1/Rb^2))

and from there the expression for the acceleration g from:

g = (c^2/L)*(df/f) such that:

g = (c^2/(2*L*f^2))*(c/(2*Pi))^2*X^2*((1/Rs^2)-(1/Rb^2))

Using the "weight" of the photon in the accelerated frame from:

"W" = (h*f/c^2)*g => "W" = T = (h/L)*df

gives thrust per photon:

T = (h/(2*L*f))*(c/(2*pi))^2*X^2*((1/Rs^2)-(1/Rb^2))

If the number of photons is (P/hf)*(Q/2*pi) then:

NT = P*Q*(1/(4*pi*L*f^3))*(c/(2*pi))^2*X^2*((1/Rs^2)-(1/Rb^2))"

My Bad ! I misinterpreted what you were saying. You are correct the change in a 1g field is quite small for these purposes.

The "g" in the formulas is the amount of acceleration needed to make the tapered cavity "look like" a cylindrical one, ie. compensated. The force (in the cavity frame) then becomes the equivalent of the "weight" of the photons in that accelerated frame.

The system acceleration that results is then the force divided by the entire system mass.

The "g" in the formulas is the amount of acceleration needed to make the tapered cavity "look like" a cylindrical one, ie. compensated

Isn't this the speed limit? When the frustum warps into the shape of a perfect cylinder (from the perspective of a photon moving toward the large end)?

If so - it seems that early on in the acceleration, one would want a shallow taper and as the acceleration limit is approached - increasing the taper (restoring the original frustum shape) would allow for further acceleration. I might have these mixed.

So whoever is building high efficiency version of this thing - you may want to design a wall that can angle, similarly to a jet engine cowl.

Thermal convection forces have plagued radiation pressure measurements since the time of Maxwell, for about 139 years and counting. There is a rich history showing this.

The shape of the Cannae device maximizes the effect of thermal convection effects.

Please notice that the thrust/PowerInput obtained by NASA Eagleworks in a vacuum is only a fraction of the one that they measured in air, which shows quantitatively the huge problem with conducting tests under ambient conditions like Shawyer in the UK and Yang in China have done. But, again, if you don't have a vacuum chamber, there are proven ways to minimize this effect that neither Shawyer nor Yang appear to have utilized.

I strongly advise against performing any Finite Element Analysis calculations unless you have an analyst available that has taken University courses in Finite Element Analysis and has practical experience with such Finite Element packages. If you want to perform FEA you must add to your team such an analyst.

EDIT: If you use the same geometrical dimensions and materials used by NASA, couldn't you use NASA's COMSOL calculations (available in this thread) to assess the frequencies and mode shapes ? (and thus avoid the need to perform any numerical calculations on your own)

Best regards,

Oh! I hadn't found the data from the vacuum test, I assume it is buried in the forum somewhere?

If there isn't strong evidence that a symmetric cavity will work, we will build a frustum. We could use EW's dimensions if we recieve funding for the variable frequency equipment. However, if we have to use a microwave magnetron we will have to do the FEA. I might be able find someone willing to help.

We don't have a vacuum chamber large enough so we will look into minimizing the effects of convection.

Thermal convection forces have plagued radiation pressure measurements since the time of Maxwell, for about 139 years and counting. There is a rich history showing this.

The shape of the Cannae device maximizes the effect of thermal convection effects.

Please notice that the thrust/PowerInput obtained by NASA Eagleworks in a vacuum is only a fraction of the one that they measured in air, which shows quantitatively the huge problem with conducting tests under ambient conditions like Shawyer in the UK and Yang in China have done. But, again, if you don't have a vacuum chamber, there are proven ways to minimize this effect that neither Shawyer nor Yang appear to have utilized.

I strongly advise against performing any Finite Element Analysis calculations unless you have an analyst available that has taken University courses in Finite Element Analysis and has practical experience with such Finite Element packages. If you want to perform FEA you must add to your team such an analyst.

EDIT: If you use the same geometrical dimensions and materials used by NASA, couldn't you use NASA's COMSOL calculations (available in this thread) to assess the frequencies and mode shapes ? (and thus avoid the need to perform any numerical calculations on your own)

Best regards,

Oh! I hadn't found the data from the vacuum test, I assume it is buried in the forum somewhere?

If there isn't strong evidence that a symmetric cavity will work, we will build a frustum. We could use EW's dimensions if we recieve funding for the variable frequency equipment. However, if we have to use a microwave magnetron we will have to do the FEA. I might be able find someone willing to help.

We don't have a vacuum chamber large enough so we will look into minimizing the affects of convection.

Thank you for the response!

This is just my opinion. It is highly doubtful that a symmetric cavity will work "on the same principle" as a frustum. Of course, if the momentum is absorbed into deforming the dielectric, it isn't increasing the kinetic energy of the cylinder in that direction. So that sort of asymmetry can cause a slight walk, but I do not think that is how the frustum works.

The frustum is a waveguide that has a strong gradient in the group velocity, near the cut-off modes, relative to the microwave photons moving inside it. This gradient is mathematically equivalent to a gravitational field and appears to be such from the frame and perspective of the moving photons.

Gravity, interpreted as a variable refractive index K, is a very wide bandwidth effect. The resonant frequencies of all particles, atomic and sub-atomic, are in equilibrium with the local ZPF. As they resonate while immersed in a variable refractive index, they "fall" toward higher values of K. The EM Drive is the same effect occuring over a very narrow bandwidth, close to the cut-off modes of the frustum where the acceleration of the group velocity is the greatest. The label on the outside should say, Gravity Inside!.

....The frustum is a waveguide that has a strong gradient in the group velocity, near the cut-off modes, relative to the microwave photons moving inside it....

As the initial photons travel towards one of the ends, and it hits the end-plate, yes it functions as a travelling wave in a waveguide. However, once the wave hits the end it gets reflected (almost perfectly since the skin depth is extremely small compared to the wavelength and hence the losses are negligible). At that point we have standing waves. The high Q of the cavity is a result of these standing waves producing resonance. So instead of a

waveguide with travelling waves having a non-zero Poynting vector transmitting energy from one end to the other,

what we have upon reflection is a

closed cavity with standing waves having a self-cancelling zero mean value (over a period) Poynting vector and there is no transmission of energy

So, the question is, do you see your mechanism as resulting into an acceleration vs. time that gives constant acceleration at constant power input, for ever and ever (which involves an energy paradox)

or

do you see your mechanism as just resulting into a one-time short-impulse or Dirac delta-function spike in acceleration only (due to the initial photons hitting the end) upon energizing the cavity ?

Presumably calorimetry would show an increased output workload when there's a mechanical displacement, compared to the static case, and likewise an accompanying increase in load drawn from the power supply.

With a potential classical symmetry break on the cards wrt N3, testing the energy symmetry should be of top priority.. cos if the virtual photon flux is donating momentum, it's also donating energy...

....The frustum is a waveguide that has a strong gradient in the group velocity, near the cut-off modes, relative to the microwave photons moving inside it....

As the initial photons travel towards one of the ends, and it hits the end-plate, yes it functions as a travelling wave in a waveguide. However, once the wave hits the end it gets reflected (almost perfectly since the skin depth is extremely small compared to the wavelength and hence the losses are negligible). At that point we have standing waves. The high Q of the cavity is a result of these standing waves producing resonance. So instead of a

waveguide with travelling waves having a non-zero Poynting vector transmitting energy from one end to the other,

what we have upon reflection is a

closed cavity with standing waves having a self-cancelling zero mean value (over a period) Poynting vector and there is no transmission of energy

So, the question is, do you see your mechanism as resulting into an acceleration vs. time that gives constant acceleration at constant power input, for ever and ever (which involves an energy paradox)

or

do you see your mechanism as just resulting into a one-time short-impulse or Dirac delta-function spike in acceleration only (due to the initial photons hitting the end) upon energizing the cavity ?

Regards,

JR

Thank you for the interesting questions, Dr. Rodal.

I do not think it will have constant acceleration for constant power input over time, because the matter of the frustum and it's source will experience relativistic effects, on mass, time and length. It takes more than a frustum to make an actual warp drive.

For now, I'm not certain that having the resonance occur inside the frustum is necessary. Resonance could occur in an exterior chamber, like pumping a "laser", something to pump the input power. Then inject a tuned coherent pulse of limited bandwidth into the frustum near it's cut-off modes. The objective being, to use the variable refractive index to amplify the momentum toward the small end. By this I mean, the momentum transforms due to the refractive index,

p => p*sqrt(c/vg)

The group velocity depends on location in the frustum and is lowest at the small end. So momentum is amplified toward the small end. The energy is not lost through resistive copper losses, it is absorbed through momentum transfer of the exponentially decaying waves that have been squeezed beyond their cut-off diameter in the waveguide. For these waves, the speed of light has come to a halt and they cannot propagate, so their momentum must be absorbed by the frustum. Where else can it go? They have crossed the event horizon, where c -> 0, the momentum can't escape.

The resonant modes are probably not so close to the cut-off and contribute very little, if anything. There is still a gradient in v group, but a much, much smaller one. I would consider this a different design, one that optimizes Q and very high energy storage over thrust, but the result will work for the same reason.

You also asked me for some equations, graphs and such. I've just started researching here and found an enormous body of information I did not know about. So... it may be a while. Any questions you may have on the PV Model and my quantum electrodynamic interpretation of it, I'm happy to assist.

I do not think it will have constant acceleration for constant power input over time, because the matter of the frustum and it's source will experience relativistic effects, on mass, time and length. It takes more than a frustum to make an actual warp drive.

...

Question: under your interpretation, the Emdrive would have a maximum speed always less than c, because acceleration would eventually decrease until maybe becoming zero due to relativistic effects on the frustum at some speed. Is that correct?

If so, what speed are we talking about? something close to c or much lower?

This topic of the Emdrive's maximum speed and the potentially diminishing acceleration is something that has appeared repeatedly in the discussions, without a clear answer yet because there is no experimental data backing it or disproving it yet.

This notion has also been rebuffed by some people, because assuming a "maximum speed" also assumes a privileged reference frame, which is a big no no in current theories.

I feel there could be a GR explanation, related to the fact that we do have an absolute speed limit: the speed of light, which is the same on all reference frames, including that of the microwaves inside the frustum.

I do not think it will have constant acceleration for constant power input over time, because the matter of the frustum and it's source will experience relativistic effects, on mass, time and length. It takes more than a frustum to make an actual warp drive.

...

Question: under your interpretation, the Emdrive would have a maximum speed always less than c, because acceleration would eventually decrease until maybe becoming zero due to relativistic effects on the frustum at some speed. Is that correct?

If so, what speed are we talking about? something close to c or much lower?

This topic of the Emdrive's maximum speed and the potentially diminishing acceleration is something that has appeared repeatedly in the discussions, without a clear answer yet because there is no experimental data backing it or disproving it yet.

This notion has also been rebuffed by some people, because assuming a "maximum speed" also assumes a privileged reference frame, which is a big no no in current theories.

I feel there could be a GR explanation, related to the fact that we do have an absolute speed limit: the speed of light, which is the same on all reference frames, including that of the microwaves inside the frustum.

Thank you. I can give you my opinion, but without the context of my latest warp drive paper, I don't know if it will make much sense to anyone. I put a link to that paper back around page 110, I think.

First off, what you said, "...the speed of light, which is the same on all reference frames, including that of the microwaves inside the frustum."

This is not true in EM, GR or the PV Model. The speed of light is only constant in "inertial" reference frames which are not constrained by matter. The frame of reference inside the frustum is non-inertial because the geometry of the waveguide causes a gradient in the speed of light "across a narrow bandwidth" of frequencies, by definition.

I believe the EM drive mimics gravity over a narrow bandwidth, inside the cavity. Anything outside the cavity is still subject to the usual relativistic effects. So it's just a thruster, but a very unique one.

The speed limit is interesting. I'm sure it will be less than c in vacuum, perhaps it would be c/K where K is the largest refractive index, at the small end. That being said...

In the PV Model, the speed of light is NOT constant. The metric coefficients of GR are interpreted as components of a variable refractive index. In regards to the notion of a preferred frame, it is "defined" not absolute. If you and I define the speed of light at the surface of the Earth to be c = 1, then in the PV model, light traveling past at higher altitude is traveling faster, c > 1 because we defined it inside a gravity well. So in the PV Model, we choose to define the refractive index K = 1, "locally" for convenience, but the vacuum is not immutable and neither are the rulers and clocks we use to measure c.

So when I say the speed limit is c/K, I'm implying that outside the EM Drive, K=1 everywhere. If you move it up or down in a gravity well, then K must be scaled to the local value. Relatively speaking, for planets, stars, black holes, K > 1. To build a warp drive that can overcome relativistic effects and go FTL relative to c "locally", then we need to inflate a warp bubble where K < 1. The EM Drive does not do this, but it's on the right track, IMO anyway.

Indeed when reading the new posts this morning, that quote from Shawyer also got my attention, but I see you already spotted it....

The Flight Demonstrator is the alu frustum I've been looking at to get the dimensions. As top and bottom plate are indeed bolted on, and those plates are unusually thick, it would not be too hard to mill them into convex and concave surfaces.

So basically, the idea of shaped endplates has been developed first in the Flight Demonstrator and not for the EMdrive2.0.

Consequently, we should see the EMdrive 2.0, not so much as a testbed, but the gathering of different research aspects into 1 design. EMdrive2.0 is not so much a theoretical design or paper on a yet to build device, as i first thought but the post-design reconstruction drawings an effective engineered device.

There is a big difference between drawings of a project device and drawings of en executed device.The value of the drawing (as far as information goes) in the last case is considerably higher....